The Stability of Relativistic Fluids in Linearly Expanding Cosmologies

Autor(en)

David Fajman, Maximilian Ofner, Todd A Oliynyk, Zoe Wyatt

Abstrakt

In this paper, we study cosmological solutions to the Einstein–Euler equations. We first establish the future stability of nonlinear perturbations of a class of homogeneous solutions to the relativistic Euler equations on fixed linearly expanding cosmological spacetimes with a linear equation of state \p=K \rho \ for the parameter values \K \0,1/3)\. This removes the restriction to irrotational perturbations in earlier work [ 15] and relies on a novel transformation of the fluid variables that is well-adapted to Fuchsian methods. We then apply this new transformation to show the global regularity and stability of the Milne spacetime under the coupled Einstein–Euler equations, again with a linear equation of state \p=K \rho \, \K \0,1/3)\. Our proof requires a correction mechanism to account for the spatially curved geometry. In total, this is indicative that structure formation in cosmological fluid-filled spacetimes requires an epoch of decelerated expansion.

Organisation(en)

Gravitationsphysik

Externe Organisation(en)

Monash University, King's College London

Journal

International Mathematics Research Notices

Band

2024

Seiten

4328–4383

Anzahl der Seiten

56

ISSN

1073-7928

DOI

https://doi.org/10.48550/arXiv.2301.11191

Publikationsdatum

10-2023

Peer-reviewed

Ja

ÖFOS 2012

103019 Mathematische Physik, 103028 Relativitätstheorie

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/aa26abb6-8f89-4a2b-960a-2fdfafb05821